‘It’s just so weird, having children,” says Bill Nighy. “The whole thing is like science fiction. Human beings make decisions and have ideas and choose their partner and it’s all so reckless and marvellous. It’s such an extraordinary thing to attempt. Maybe it’s just my age, but I just think of all the energy involved to have and raise children, you know?”

I hear him gliding down the street, phone in hand, offering some sort of gorgeous apology to a cafe door. “And then there’s this human being who turns out to be somebody quite independently of whoever might have been involved in their creation. They’re this completely other thing. And they’re also, in the case of my grandchildren, edible.”

Nighy is a highly covetable grandfather. His date to the Oscars two years ago was a stained Sylvanian bunny (“My granddaughter’s schedule intensified,” he explained, “and I was charged with rabbit-sitting responsibilities”). This year he has lent his voice to no fewer than five children’s animations. And now he’s playing the real-life gynaecologist who pioneered IVF.

“It’s a very obvious remark,” he says, “but the world is divided between people who’ve had children and people who haven’t. Not that it’s a criticism of either group, but nothing can quite prepare you for the moment where they hand you a human being and say, this is yours, you are now their custodian.

“And as soon as you take the weight of the baby, you’re like, ‘Oh, I see, it’s entirely about this now. It’s not about me.’ So it hopefully unplugs some of our unhelpful self-absorption. There’s something outside of yourself to concern yourself with. You go down the billing.” The birth of his daughter 40 years ago was, he concludes, “the most significant thing that has ever happened to me”.

Joy is an origin story for the procedure that enabled millions of people also to become parents. It’s a movie about three good people – Dr Patrick Steptoe (Nighy), Dr Robert Edwards (James Norton) and lab technician Jean Purdy (Thomasin McKenzie) – trying to do a good thing, which everyone knows they manage. Yet it is as gripping as a thriller. Because, explains writer Jack Thorne, it has the structure of a sports movie. The key players “were a genuine team and it cost them to be part of that team. It’s just their season ran from 1968 to 1978.”

1978 was the year the first IVF baby, Louise Brown, was born. In Joy, we don’t encounter her parents until the final reel; the film juggles primal emotions and immense restraint. One touchstone for its director, Ben Taylor, was First Man, the Neil Armstrong biopic starring Ryan Gosling. “Even the overblown trailer finishes with a countdown to liftoff,” he says. “Every second is interspersed with cuts of him and his family.” Yet the step for mankind managed in Joy is arguably more immense. “Going to the moon is one thing but what they did is more important.”

They shot it in the shadow of Oppenheimer: another film, says Taylor, with “a lot of theory, a lot of lab work” – but a more obviously cinematic climax. Filming all the chat took ages, he says, “but then you’ve got James Norton with a pipette. And you can’t just bosh it off in 10 minutes. You want to worship it because it’s the magic of the film.”

So embryos are fertilised in ecstatic closeup. The Lark Ascending booms on the soundtrack. It’s as lush and lyrical as a conventional baby-making scene, just with rather less nudity. “It was a relief there were no sex scenes,” says McKenzie. “That it’s a film not about sex.” She has just finished a film in which her character is celibate. “I was like, ‘Amazing! love it!”

The simplicity of the science surprised Nighy. “The idea of fertilising an embryo outside of the body seemed unachievable. It’s such a profound development yet the actual mechanics of it are not that complicated.” “It’s incredibly binary,” agrees Taylor. “And it’s still very much based on what these three people were doing in a shack in Oldham 47 years ago.”

Joy is Taylor’s first film; he cut his teeth on TV such as Catastrophe and Sex Education. “I’ve loved everything I’ve made,” he says, “but this was the one where I knew I had to make it.” He and his wife have two children conceived by IVF; he caveated job offers with the warning that the film might be too painful to work on for anyone who had had a less happy outcome.

“It was the most emotional rehearsal process I’ve ever had in a film,” agrees Thorne. “So many tears all the way through.” Including for him and his wife and co-writer, Rachel Mason. “Things came to light that probably wouldn’t have,” he said. “Rachel told me she’d decided to leave me if we didn’t have a kid.”

“Because the issue was my issue,” says Mason quickly. “So I felt incredibly guilty: Jack could be with someone else and not go through all this.” Mason now runs a support group for women undergoing fertility treatment, and those experiences are channelled into those scenes in the film concerning the Ovum Club, the self-named group of female volunteers who took part in the gruelling trials, motivated by a desire to help future women desperate to get pregnant – and the glancing hope they themselves might.

Had they not had their son, says Mason, she couldn’t have written Joy. “The trauma, the grief: it’s in you, it never goes. It’s just a darkness. It feels weird saying it, but I still have a reaction to someone else’s pregnancy announcement.” The upset and unwelcome jealousy of others is, she says, “still quite raw”.

“Capturing that shard of ice that comes when you’re dealing with infertility was really important,” says Thorne. “And I think we only caught that because of what we’d been through.”

The film also explains how Purdy – whose crucial role was long diminished, Rosalind Franklin-style – was spurred in part by her own endometriosis. “She wasn’t able to have children,” says McKenzie. “And because of that, she felt like she didn’t deserve love. She’d grown up in a very religious household and the expectation placed on her was to have children and she couldn’t do it. So she knew how that felt, and the humanity in her drove her to want to help other women.”

McKenzie, 24, gives a remarkably mature performance as a woman whose work meant she was shunned by her church-going mother, Gladys (Joanna Scanlan). “The question of whether I’m capable of being a mother is something that’s always been on my mind,” says McKenzie. “Growing up, a lot of pressure is put on girls to be mothers. Our first toys are baby dolls. I grew up hearing that term: ‘baby-bearing hips’.

“So I wanted to bring that to the forefront, especially because it’s so relevant to what’s happening today with American politics and women’s rights, women’s health and Roe v Wade.” She invokes Edwards’ argument: infertility is a medical condition no less deserving of treatment than any other. “Technology is so advanced now that we can do insane operations like laser eye surgery, so why is it not OK for women to have more power over their bodies? It’s men who seem to want to control that, but are totally fine with the technology to remove tumours.”

The cast and crew have little time for sceptics, either of today or half a century ago. “I remember there was friction, static,” says Nighy, of the 1970s stew of misinformation and misplaced anxiety. “But no one was playing God. There is no God, so you can’t play God.”

Before he read theology at university, Norton attended a Catholic boarding school, an experience that has not made him more forgiving of intolerance. “Within the monastery there were beliefs around contraception and female priests and homosexuality I did not agree with. Just because they were embedded in an institution of the church, that didn’t make it more palatable.”

Something beeps in the background of our video call. Norton has type 1 diabetes, which necessitates a pump and a sensor and – if he’s on stage for a while – strategically scattered snacks. “I’m very aware of the importance of medical advancement and pharmaceuticals being given the attention and investment they require,” he grins. “There’s nothing in the progress of science that I feel threatened by.”

Being in a film that highlights this incredible homegrown breakthrough makes him feel “immensely proud”, he says, as well as “very reassured” he doesn’t live in the US where the IVF procedure has been variously “politicised … hijacked … and kind of weaponised”.

Joy was not conceived to be political. But its accidental relevance is, says Taylor, “exciting”. “It can’t come out soon enough for me because it hopefully just shines a light on how simple and how essential this process is and how widely people are affected by infertility.”

Nighy expresses discreet optimism it will have some effect. “Possibly marginally. To have a film that describes in detail the people and the events, rather than just reacting to an idea.”

Thorne is less moderate. “The battle in the US is savage and it’s horrific,” he says. “Doctors being scared to do their jobs is the worst thing imaginable. Yet remember that in this country, Louise Brown was born of two working-class parents who were properly supported. That doesn’t happen now. You can do IVF if you can afford it or live in the right postcode. We did seven rounds – that would be impossible on the NHS. So while the political questions for the US are interesting, there are also political questions for us.”

The women in the waiting room in Oldham came from all economic and ethnic backgrounds, says Taylor. Yet it’s now “the pursuit of the middle classes. It’s shocking to imagine how few people can continue the journey after their first attempt. The darker side of it in this country is how exclusive that club can be.”

His voice wobbles. He’s shooting in Albuquerque and hasn’t seen his children for four months. “It’s so indulgent to say, as someone who’s seen the film 200 times, but there are moments in it that still overwhelm me. There’s just something so beautiful about this idea of sacrifice and the universal desire to have a family.”

“People can and do live incredibly fulfilling lives without children. And that should be a choice. But for me, it beats everything. It feels like as close to the embodiment of love and fulfilment as I can imagine.”

In the film, the character who best articulates this is also the one most opposed to the project succeeding. “When you look back on your life,” Gladys tells Jean at something of a critical moment, “mostly all you can see is failure. But the one thing you can’t see failure in is your children because they’re always beautiful.”

Taylor composes himself. “It’s incredibly easy to say ‘I’ve got a problem with something’ if somebody else is after it and you’ve already got it,” he says. “Parents who have a moral objection to somebody else wanting to be a parent I find excruciating.”

Nighy, still gliding down the street, weighs nature and nurture and what parenthood means to him. “There is a simplistic way of looking at it,” he says, “which would suggest that children are the meaning of life. I see them as beautiful, my daughter and my grandchildren. And I do wonder how much of this is biology or narcissism or self-interest or self-absorption.

“But actually, they’re just fabulous. It’s nothing to do with me. I’m just a big fan. They’re funny and kind and smart and decent. I’m not very self-aware to be honest, but I really don’t take any personal credit. I’m pleased about certain elements, but I don’t think they’re as a result of my brilliant contribution.”

Would he be the same person had he not had a child? “I’m halfway down a very strong cup of coffee,” he says, “which might persuade me into positions I have no right to hold, and I’m not kidding, I’m super-vulnerable to coffee, but I don’t see them as a representation of me but sort of in spite of me.”

He snorts that familiar snort, which may or may not have been passed down the genetic line. “I’m quite astonished to be anybody’s father. It’s a relief. I like it. I like it rather better than being me.”